Land Abundance, Risk and Return:A Heckscher-Ohlin Linear Programming Approach to FDI1

Peter K. Schott2

Ph.D. Candidate in Business EconomicsAnderson Graduate School of Management, UCLA

pschott@ucla.edu

May 30, 1998Comments Welcome.

Abstract

Why is investment in human and physical capital in Latin America lower than in the faster growingeconomies of East Asia? Is this phenomenon and Latin America’s generally higher income inequality animportant consequence of the input requirements and price variability of the regions’ products. To helpanswer these questions, this paper explores a Heckscher-Ohlin linear program incorporating real-worldinformation on input intensities and product prices. It demonstrates: (1) that land abundance may deterskill accumulation and raise income inequality; (2) that insufficiently diversified production may createunfavorable capital risk-return profiles for resource rich countries, deterring investment; and (3) that theeffect of such unfavorable profiles may be mitigated by international investors’ desire for a balancedportfolio of diversification cone assets. More generally, the paper provides an nice example of how amulti-sector, multi-factor linear program can be used to gain insight into a variety of pressing problems ininternational trade and development.

Key words: Heckscher-Ohlin; Investment; Factor Price Risk; Linear Programming SimulationJEL classification: F1.

1Many thanks to Ed Leamer. Thanks as well to Hugo Maul, Sergio Rodriguez and participants of the 1998Workshop for Empirical Research on International Trade and Investment Conference.2Anderson Graduate School of Management at UCLA, 110 Westwood Plaza, Suite C501, Los Angeles, CA 90095-1481; tel: (310) 825-8207; fax: (310) 206-2002; email: pschott@ucla.edu; website:http//:www.personal.anderson.ucla.edu/~peter.schott.

Peter K. Schott

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Land Abundance, Risk and Return: A Heckscher-Ohlin Linear Programming Approach to FDI

1 Issues

Do land abundant countries have riskier capital rewards, and does this prevent them from

attracting global investment? Does land abundance delay the emergence of skills, further delaying the

development of manufacturing sectors integral to reducing income inequality? This paper seeks an

answer to these questions by pushing the well-worn Heckscher Ohlin (HO) model in a new direction to

provide insights about capital risk and return. It accomplishes this task by constructing a HO linear

program employing real world data on factor inputs, endowments, product prices and price uncertainty.

This linear program provides a simple framework, based upon fundamentals, for understanding the

investment-inhibiting effects of insufficient manufacturing diversity. In addition, thought experiments

based upon its output demonstrate that global investors’ desire for a balanced portfolio of diversification

cone assets may mitigate the investment-deterring effects of agricultural dependence, depending upon the

covariance of capital returns by cone. More generally, the discussion of the modeling process provides a

nice example of how a multi-sector, multi-factor linear program can be used to gain insight into a variety

of pressing problems in international trade and development.

Though many previous studies have researched the effects of macroeconomic volatility on

investment, growth and other performance measures (see, for example, the review in Sevren (1996)), few

have investigated its root causes. An exception is IADB (1995), which, like the research below, points to

the importance of primary product export concentration in addition to external shocks, government policy

and inadequate financial institutions. Even in that study, however, the explicit link between factor

endowments, input intensities and price variability – the consideration of which is so natural for a trade

economist – has been ignored. In the theory and evidence sections to follow, we hope to make this

relationship clear.

Peter K. Schott

3

The remainder of the paper is organized as follows: section 2 illustrates how price risk translates

into factor risk within the factor proportions model; section 3 illustrates how these concepts can be

brought to life by a Heckscher-Ohlin linear program; and section 4 concludes.

2 Theory

2.1 How Does Price Risk Affect Factor Rewards? 1

How does price variability affect reward volatility, and how might diversification out of

agriculture and into manufacturing mitigate the risk to capital? Figures 2.1.1 and 2.1.2 help provide some

intuition for this question by illustrating graphically the link between product price and factor reward

uncertainty within the context of a Leamer (1987) triangle. Recall that this “endowment triangle” is the

simplex formed by intersecting the positive orthant of a three-dimensional factor space with a plane so

that the coordinate axes are represented by the corners of the simplex and industry-input and country-

endowment vectors are represented by points within it.

1 The theory in this section is developed more fully in Leamer, Maul, Rodriguez and Schott (1998).

Peter K. Schott

4

Figure 2.1.1: The Affect of Price Risk on Rewards in a 3xN Model

Labor

Capital

Land

Apparel

MangosFood

Labor

Capital

Panel 1 Panel 2

Land

Mangos

Apparel

Figure 2.1.2: Detail of the Affect of Price Risk on Factor Rewards in a 3xN Model

Price Increase

Price Decrease

(Wage Increase)

(Wage Decrease)

No Change

Apparel

Mangos

Textiles

Apparel

MangosFood

Panel 1 Panel 2

No Change

Price Decrease(Wage Decrease)

Price Increase(Wage Increase)

Labor Labor

Capital Capital

Assume we have three factors – land, labor and capital -- and three sectors. In the first panel of

figure 2.1.1, the three sectors are mangos, apparel and textiles, while in the second panel they are mangos,

processed food and textiles. Careful inspection of the figure reveals that the production of apparel and

Peter K. Schott

5

textiles requires only physical capital and labor, while the cropping of mangos and food processing

involve the use all three factors. Recall that the particular simplexes drawn (and anchored by the

appropriate factor rewards) in each panel of the figure have been determined uniquely by each triplet of

black dots. These dots represent tangency points between the simplexes and industry "iso-bowls", akin to

the tangency of price lines and isoquants in the 2xN case. 2 Since approaching a corner of the endowment

simplex along a ray emanating from that corner represents an increase in the use of that factor, holding

the concentration of other factors constant, inspection of the figure also reveals that textiles use more

physical capital than apparel, and both use the same ratio of land to labor, which is zero. Thus, the

industries in panel 1 are more manufacturing-diversified than those in panel 2 because fewer products

depend upon land.

Now suppose that the price of mangos varies but that the prices of apparel and textiles remain

constant. We can represent this price movement graphically in figure 2.1.2 by sliding the Mangos

industry input dot along a ray emanating from the origin. Movement toward the origin represents a price

increase (i.e. fewer factors for the same dollar output) and vice versa. What happens to factor rewards?

As illustrated in the first panel, mango price movement stimulates fluctuations in the reward to land,

which drops when the price of mangos falls (light gray circle) and increases when the price of mangos

rises (dark gray circle), but the rewards to capital and labor do not change because the mangos-apparel-

textiles cone of diversification merely pivots on the bottom edge of the simplex. Note that though this

discussion has focused on the nominal rewards, this is equivalent here and below to focusing on real

rewards if we normalize by the price of apparel, which is assumed to be constant.

If a country’s production is not sufficiently diversified into land-independent manufacturing, as in

the second panel of figure 2.1.2, the return to capital is “imperiled” by mango price volatility. Thus, as

2 Actually, for simplicity of exposition, the particular Leamer triangle exhibited here relies upon fixed input

technologies (i.e. “iso-corners” rather than “iso-bowls”). Though the mathematics becomes more complicated with

non-Leontiff technology, general substantive conclusions should hold.

Peter K. Schott

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shown, fluctuations in the price of mangos tilt the high capital risk mangos-apparel-food processing cone

of diversification in such a way as to shift the wages of all three factors. These shifts in factor rewards are

indicated by the light and dark gray circles along each factor’s vertex, where as above light gray means

mango price decrease and dark gray means mango price increase. Indeed, as illustrated in figure 2.1.3,

the reward to capital is insulated from product price variability so long as the sectors without volatility

have identical land to labor input requirements. Geometrically, this is tantamount to lining up along a ray

emanating from the capital vertex. This type of diversification occurs most intuitively in the first panel of

figure 2.1.3, where manufactured goods all have zero land to labor requirements, but can occur with three

natural resource commodities as well, as illustrated in the third panel. Of course, the insulation of capital

in the third panel can be overturned if more than one commodity price is highly volatile.

Figure 2.1.3: Conditions Under Which Capital Returns areInsulated and Imperiled From Mango Price Volatility

Mangos

Apparel Textiles

Land

Capital

Mangos

Apparel

Food

Mangos

Beans Food

ImperiledInsulated Insulated

Land Land

Capital CapitalLaborLaborLabor

What are the implications of high capital risk cones for development? Figure 2.1.4 plots possible

development, or capital accumulation paths of two types of countries, land abundant and land scarce, in

an n-good world.3 The upper arrow in the figure represents the land abundant development path, while

3 Note that the manner in which the industry-input points are connected to form cones of diversification depends

upon product prices: in general, the more expensive a commodity, the larger its region of production (Leamer 1987).

In figure 2.1.3, for example, apparel and food are assumed to be relatively dear due to the large swaths of the

simplex in which they are produced. With n goods, a simplex can be filled with many cones of diversification, each

Peter K. Schott

7

the lower arrow traces out the land scarce path. Though both countries must pass through the two high

risk cones, which are shaded in the figure, these cones comprise a much larger portion of the land

abundant country’s development path. To the extent that international investors avoid allocating capital

to countries in high risk cones, land abundant countries may become “trapped” in the cones proceeding

them. Land scarce countries, able to skirt through high risk cones relatively quickly by relying on

domestic savings, on the other hand, may face no such obstacle to their development. As a result,

whereas land scarce countries will move from handicrafts and apparel on to textiles and machinery, land

abundant countries may remain undeveloped, producing handicrafts, apparel and beans indefinitely. This

intuition provides the motivation for the simulation scenarios below. One of the implications of the linear

program is that land abundance does indeed delay industrialization.

Figure 2.1.4: The Affect of High Risk Cones on Development

Apparel

Food

Land

Labor CapitalTextiles MachineryHandicrafts

PeasantAgriculture

Mangos

HighRisk

HighRisk

Processing

(Beans)

LandAbundant

Path

LandScarce

Path

of which, through zero profit conditions, has three unique factor rewards given the three product prices which

anchor it, similar to the 2xN case. In this way, if there are no factor intensity reversals, the Factor Price Equalization

theorem can be generalized to higher dimensions. With respect to risk, the diagrams above and calculations in

section 3 below make clear that factor risk equalization holds as well.

Peter K. Schott

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To highlight a possible implication of this delay, figure 2.1.5 plots an estimated 1990 Gini

coefficient surface over a Leamer (1987) endowment triangle anchored by labor, cropland and capital.

This surface is estimated by first plotting each sample country in the endowment triangle and then taking

factor-space weighted averages for each point on the simplex. In the figure, both shading and elevation

(in the three dimensional view) are used to represent income inequality. Low Gini’s are represented by

dark gray and low elevation, while the highest Gini’s are represented by light gray and peaks. One reason

for the persistently high income inequality in Latin America, for example, may be its inability to attract

enough capital to move towards the capital vertex of the simplex.

Figure 2.1.5: Income Inequality and Endowments

Cropland

Labor Capital

Cropland

Capital

Labor

30

Gini Scale

60

We can tell the same story about price uncertainty and capital risk algebraically. The Stolper-

Samuelson mapping of goods prices into factor prices is built from zero profit conditions equating

production costs to product prices:

A’w = p

Peter K. Schott

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where A is the matrix of inputs per unit of output, w is the vector of factor rewards and p is the vector of

product prices. If the number of factors equals the number of products (i.e. A is square), and if there are

no linear dependencies among the columns of A, then this system can be inverted to solve for the factor

rewards as a function of factor prices:

w = (A’)-1 p.

From these equations and from the mean E(p) and covariance matrix Var(p) of prices, we can

solve for the corresponding mean and covariance matrix of the factor returns:

E(w)= (A’)-1 E(p)

Var(w) = (A’)-1 Var(p) (A)-1

From this system of equations we seek conditions under which the mean return to capital is high and the

variance is low. More generally, we want to determine the optimal global allocation of capital across a

set of “diversification cones” when the cones differ in terms of economic structures A and price

uncertainty Var(p). In particular, we would like to answer the question: how should global capital be

allocated across natural resource rich and natural resource poor countries? The answer might be “not

much to resource rich countries” either because the high returns they offer do not compensate for the

greater risk or because their risk-return profiles do not offer diversification incentives. This would be a

force for keeping the natural resource rich countries in a permanent state of underdevelopment.

The equation for solving for means and covariances is easy to write down, but not so easy to

understand. A first step toward understanding comes from a careful examination of the two-dimensional

case with the inputs being capital and labor. Then the vector of factor rewards as a function of product

prices is:

Peter K. Schott

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w

w

A A

A A

p

pA A A A

A A

A A

p

pK

L

K L

K LK L K L

L L

K K

=

= −

−−

−

−1 1

2 2

11

21 2 2 1

1 2 1

2 1

1

2

( )

Since it is only relative prices that affect real rewards, we might as well normalize by the second price and

solve for

Var w p A A A A A Var p pA

A

A

A

A

Var p pK K L K L LL

K

L

K

L

( / ) ( ) ( / )/

( / )2 1 2 2 12

22

1 21

1

1

2

2

2

1 2

1= − =

−

−

The message of this equation is conveyed by the denominator: diversity of capital intensities is a source

of stability for capital returns. Countries that produce goods that are very similar in capital intensities

have capital returns that are very sensitive to relative prices.4

2.2 Assessing Actual Product Price Variability

By focusing on mango price volatility, the previous section implied that natural resource-based

commodities have greater price volatility than manufactured items. One method of discerning this

differential volatility is to estimate and compare price forecasting standard errors for a variety of products.

The use of forecasting standard errors rather than sample standard errors is designed to mimic the

behavior of entrepreneurs who use historical time series data to predict future prices. They are calculated

in two stages. The first stage is to run an Ordinary Least Squares regression of the log of each price index

(US PPI deflated) of the form

4 Although the labor-intensity of the first good enters the equation, that number and also the price variance depends

on the units. It seems best to choose units of the products such that the labor input is one in both sectors.

Peter K. Schott

11

p pt t t= + +−α β ε1

where pt is the log of the deflated price index of a given commodity at year t. The second stage is to use

the estimated coefficient, β , and regression standard error, σ , from this regression to calculate the

forecasting standard error,

f sn

n

s

= +

=

−

∑σ β2 2

1

1

1

where s is the number of years in the future to be forecast. This measure of volatility would equal the

sampling standard error if β =0, that is if prices behave like a random sample out of a distribution, without

trend and without serial correlation. But with a trend or with serial correlation, the simple standard error

can give a very misleading idea of the real uncertainty.

Table 2.2.1 provides a summary of 5 year forecasting standard errors, estimated on price indexes

from 1970 through 1994 (1970=1), for representative goods from each of 10 aggregate product groupings

outlined in Leamer (1984). These groupings are:

Abreviation DescriptionPET petroleum productsMAT raw materialsTRP tropical productsANL animal productsCER cereals and grainsFOR forest productsLAB labor intensive manufacturesCAP capital intensive manufacturesMCH machineryCHM chemicals

Peter K. Schott

12

Most of these categories are broken down further in the table to provide a sense of how uncertainty varies

within aggregates (note that TRP and FOR provide examples of both crop and manufactured products).

For each of the categories except PET and FOR-crop, the highest and lowest standard errors for each

group are reported along with a representative commodity. The representative commodities had

forecasting standard errors either equal or very close to the average standard error of the group. High,

low and representative manufactured products are at the four digit US SIC level of aggregation.

Table 2.2.1: Five Year Forecasting Standard Errors for Each of Ten AggregatesGroup SubGroup Hightest Std Error Lowest Std Error Representative Good

PET - - - - 1.58 Crude Petroleum

MAT 0.44 Lead (US) 0.10 Manganese 0.27 Tin (London)

TRP Crop 1.24 Sugar 0.08 Bananas 0.51 Coffee (Cent Amer)

Manufactured 0.38 Sugar Processing 0.03 Canned Fruit 0.25 Roasted Coffee

ANL 0.84 Wool 0.18 Beef 0.39 FishCER 0.68 Lindseed 0.26 Maize 0.40 Wheat

FOR Crop - - - - 0.38 Tropical Timber

Manufactured 0.32 Specialty Sawmill 0.02 Paper 0.09 Hardwood Flooring

LAB Furniture 0.06 Metal Office Furn 0.03 Mattresses 0.05 Wood House Furn

Apparel 0.18 Leather Goods 0.02 Male Neckwear 0.04 Male Underwear

CAP Rubber 0.06 Rubber Footwear 0.03 Rubber Products 0.04 Reclaimed Rubber

Textiles 0.14 Yarn 0.03 Tufted Carpet 0.07 Warp KnitIron/Steel 0.24 Primary Smelting 0.05 Brass 0.10 Copper Rolling

Metal Manuf 0.11 Ornamental Work 0.02 Boilers 0.07 Metal Cans

MCH Non-Electrical 0.09 Mining Equipment 0.03 Compressors 0.06 Hoists

Electrical 0.09 TV Receivers 0.03 Fans 0.05 Refrigerators

Transportation 0.25 Tanks 0.03 Trailors 0.07 Motor Vehicle Parts

Professional 0.07 Measurment Devices 0.03 Surgical Equipment 0.05 Othrapedic Equipment

CHM 0.18 Carbon Black 0.04 Synthetic Fibers 0.11 Resins[1] Forecasting standard errors for commodity groups based upon annual spot market prices, 1970-1993.

[2] Forecasting standard errors for manufactured goods errors based on U.S. shipment deflators in Bartelsman, Becker and Gray (1997).

[3] Price indexes for shaded commodities graphed in figure 5.

As indicated in the table, two trends stand out. The first is that natural resource prices are in

general more uncertain than those of manufactured commodities, with crude oil and sugar being

exceptionally volatile. The second trend is that manufactured commodities tend to be more volatile the

more closely they are associated with raw materials. Thus, for example Sugar Processing, Leather Goods

and Primary Smelting stand out within their respective aggregates. Both trends motivate our focus on the

contribution of natural resource commodity price uncertainty on capital reward risk.

Peter K. Schott

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For a graphical view of the same data, figure 2.2.1 traces the deflated price indexes of the shaded

representative goods in table 2.2.1 from 1970 to 1994 (1970=1). This figure highlights the relative

stability of manufactures as well what appears to be a general decline in non-petroleum natural resource

commodities since 1980. Note that the lower panel of the figure zooms in on the non-petroleum series for

a better view of relative movements. Figure 2.2.2, which plots the same indexes for seven of the ten

indexes 1950 to 1970 time period, indicates that both CER and TRP experienced similar declines earlier

during the 1950s, while MAT seemed to experience a rise during the 1960s, perhaps due to the US

military buildup associated with the Vietnam War.

3 A Numerical Simulation (Linear Programming) Model

Though Leamer’s triangles are a very useful device for gaining intuition, they do not offer the

kind of quantitative detail we’d like for answering the sorts of questions posed in the introduction. As a

result, we turn here to the linear programming problem that lies behind these triangles, and report

solutions to specific numerical programming problems using as inputs real world data on input intensities,

product prices and their volatility. More specifically, the linear programming problem that underlies the

figures is:

Choose output mix q to maximize the value of output = GDP = p’q, subject to the resource

constraint Aq ≤ v,

where q is the vector of outputs, v is the vector of factor supplies, A is the matrix of input/output

coefficients and p is the vector of world prices. The corresponding dual program is:

Choose factor costs w to minimize total costs = GDP = w’v, subject to the non-positive profit

constraint A’w ≥ p.

Peter K. Schott

14

We will use this framework to study what happens to differentially endowed economies as they

accumulate capital. Before discussing results in section 3.2, the next section will discuss how the data

used by the simulation was gathered and refined.

3.1 Simulation Assumptions

Table 3.1.1 summarizes data gathered on manufacturing industry factor requirements and prices,

all normalized by a unit of labor. Capital per worker (k/l) and value added per worker (va/l) for each

three digit ISIC sector are calculated as the labor-weighted average of the cross section of countries for

which data is available in 1990, with the sixth column of the table indicating the number of countries

included in the averaging. The source of the data, including the gross fixed capital formation series from

which a real capital stock per sector was computed, is the UNIDO INDSTAT3 database from the United

Nations. Because the type of countries for which information is available through this database tends to

correlate with capital intensity, we expect the capital and value added figures to be more representative of

developed than developing countries.

Peter K. Schott

15

Table 3.1.1: Factor Content of Manufacturing Sectors, Sorted by Tertiary Education Input, 1990isic industry k/l va/l av workers n none/l pri/l sec/l ter/l US CPS industry code (education only)353 Pet 60,348 317,074 10,683 25 0% 0% 40% 60% 200351 IndCh 22,865 96,088 55,485 33 0% 1% 42% 57% 192385 Prof 5,273 66,788 57,736 28 0% 7% 38% 55% 371,372,380,381,382342 Print 5,804 61,637 125,194 29 0% 1% 47% 53% 171,172352 OthCh 10,459 107,010 64,983 26 0% 2% 48% 50% 181,182,190,191314 Tob 2,955 132,305 16,141 23 0% 0% 51% 49% 130383 Elec 7,963 55,824 236,591 27 0% 1% 51% 48% 340,341,342,350384 Trans 9,367 63,129 199,365 29 0% 1% 53% 46% 351,352,360,361,362,370382 Mach 5,590 57,026 253,195 27 0% 2% 55% 43% 310,311,312,320,321,322,331,332313 Bev 11,406 85,836 22,515 30 1% 3% 54% 42% 120355 Rub 7,507 41,602 42,153 27 0% 3% 59% 38% 210,211356 Plas 7,262 52,135 87,219 24 1% 3% 58% 38% 180362 Glass 8,765 49,415 24,139 24 0% 3% 63% 34% 250354 PetCoa 8,309 72,277 6,478 19 0% 0% 68% 32% 201341 Paper 18,225 70,077 58,694 33 0% 2% 66% 32% 160,161,162311 Food 5,923 47,859 195,250 33 1% 5% 63% 31% 100,101,102,110,111,112381 Metal 5,402 45,405 143,469 32 0% 4% 66% 30% 281,282,290,291,292,300,301361 Pott 5,180 25,133 17,595 31 0% 6% 64% 30% 261,251,252372 Nfeff 14,473 64,013 31,723 24 0% 4% 68% 29% 272,280369 Nmet 7,842 54,272 63,753 24 0% 5% 66% 29% 262371 Iron 12,577 58,887 72,092 31 1% 2% 69% 28% 270,271390 Oth 2,767 40,413 37,101 28 8% 8% 57% 27% 390,391,392331 Wood 4,077 30,263 57,289 33 1% 5% 68% 25% 230,231,232,241321 Tex 3,712 23,932 142,610 34 1% 4% 74% 22% 132,140,141,142,150324 Foot 1,201 18,640 21,080 28 1% 3% 74% 22% 221332 Furn 2,801 36,671 49,863 27 0% 7% 73% 20% 242322 App 904 18,516 119,383 28 2% 13% 69% 16% 151323 Lea 2,067 20,917 16,488 26 1% 8% 77% 15% 220,222

Notes:[1] Capital, value added and worker data is from UNIDO database, based on n countries; k/l and va/l are labor weighted averages of the n countries avaiable.[2] Education input requirements extrapolated from from US Current Population Survey Data, 1989-1991.[3] Real capital stock is 15 year accumulated, depreciated (13.3%) and deflated (US PPI) gross fixed capital formation by sector.[4] Education input requirements are based upon averages of indicated three digit sub sectors. Obvious outliers to these averages are shown in table 3.2.[5] k=capital; l=worker; none=no education; pri=primary education; sec=secondary education; and ter=tertiary education.

Educational inputs are extrapolated from responses to the 1989-1991 US Current Population

Survey (CPS). Respondents to these surveys indicated both their educational background and the

industry within which they work (at the three digit, CPS level of aggregation). The proportion of

respondents in each of the following years-of-schooling categories is used to approximate the educational

requirements of a given three digit sector. These are clearly representative of advanced developed

countries, not developing ones. We will say more about how we deal with this aspect of the data when

we report the results.

Years of School Level Abbrev<1 no education none1-6 primary pri7-12 secondary sec>12 tertiary ter

Peter K. Schott

16

Three digit CPS sectors are averaged as indicated in the table to estimate the educational

requirement for a given three digit ISIC category. Note that Petroleum, Industrial Chemicals and

Professional goods require the greatest proportion of tertiary educated workers, while Leather goods,

Apparel and Furniture require the least. In some cases, there were obvious outliers within the set of three

digit CPS sectors corresponding to a given ISIC sector. One of the CPS sectors used for the Machinery

industry (ISIC 382), for example, is Computers (CPS 322). While average tertiary requirement for

Machinery is 43%, that for computers is 74%. Thus, to complement table 3.1.1, several outliers are noted

in table 3.1.2.

Table 3.1.2: Obvious Outliers to Education Input Requirements in Table 3.1isic industry sub-industry sic none/l pri/l sec/l ter/l385 Prof Photo 380 0% 1% 34% 64%383 Elec Radio,TV 341 0% 1% 40% 58%383 Elec House Appl 340 0% 2% 67% 31%384 Trans Space, etc 362 0% 0% 29% 70%384 Trans Aircraft 352 1% 1% 44% 53%382 Mach Office Mach 321 0% 2% 46% 52%382 Mach Computers 322 0% 1% 26% 73%355 Rubber Tires 210 0% 1% 54% 46%381 Metal Ordnance 292 0% 2% 53% 46%361 Pott Pottery 261 0% 5% 60% 35%331 Wood Wood Bldg 232 0% 1% 62% 36%

An interesting feature of table 3.1.1 is that the manufacturing industries allied most closely with

natural resources (i.e. Wood, Furniture, Food, Beverages and Tobacco) have relatively low tertiary

education requirements. This characteristic is consistent with the notion that the types of manufactured

goods resource abundant countries produce during the earlier stages of industrialization do not demand

high levels of education. This point will be underscored in the simulation results below.

Table 3.1.3 summarizes assumptions about agricultural input requirements gathered from field

research in Guatemala. A noteworthy feature of this data is the relatively high per worker capital

intensity of some of the perennial crops. Because many perennials require several years of waiting before

Peter K. Schott

17

harvesting can take place, much of the capital in perennial crop abundant countries can be absorbed by

land, delaying the emergence of manufacturing. For more detail on this effect or how the agricultural

data were calculated, see Leamer, Maul, Rodriguez and Schott (1998).

Table 3.1.3: Factor Content of Agricultural IndustriesAll figures are in $1990 Beans Sugar Corn Rubber Mangos Cotton Coffee Cashew Citrus Rice BananasYields (tons/ha) 0.59 3.90 4.55 1.25 59.98 1.19 1.62 6.85 413.05 5.20 39.00

Average Price 1970-1980 415 420 126 1171 77 1729 3312 385 17 467 657Value of Production 243 1637 572 1464 13303 2056 5365 2633 7221 2429 25637Waiting Capital 0 564 0 6320 3190 0 6535 6348 17411 0 21217Machinery Capital 20 243 670 0 229 1660 0 0 71 1681 845Labor Requirements (man-days) 51 116 32 273 119 56 200 153 253 12 117Labor Requirements (man-years) 0.17 0.39 0.11 0.91 0.40 0.19 0.67 0.51 0.84 0.04 0.39

SUMMARY DATAWaiting Capital (r=.1) / Worker 0 1459 0 6942 8064 0 9783 12446 20637 0 54273Machinery Capital / Worker 119 628 6254 0 580 8863 0 0 84 43326 2163Total Capital / Worker 119 2087 6254 6942 8644 8863 9783 12446 20721 43326 56436Production / Worker 1432 4235 5343 1608 33624 10979 8032 5162 8559 62624 65578Hectares / Worker 5.88 2.59 9.34 1.10 2.53 5.34 1.50 1.96 1.19 25.78 2.56Capital / Hectare 20 807 670 6320 3420 1660 6535 6348 17482 1681 22063Production / Capital 15.87 2.68 1.12 0.30 5.13 1.64 1.08 0.54 0.54 1.91 1.53

3.2 Simulation Results

As a first pass, rather than attempting to model several different educational factors (e.g..

primary, secondary and tertiary education), we model workers as possessing either high or low skill.

With respect to the input intensities described in table 3.1.1, high skill corresponds to tertiary educated

workers while low skill refers to any schooling less than that. One reason for selecting this categorization

is to mitigate the effect of using US data on education inputs for what is essentially a developing country

simulation: it seems reasonable to assume that developing country input requirements are split between

high and low skill in roughly the same manner that US requirements are split between college and no

college. A second reason for choosing to work with only two skill categories at this point is to ease

interpretation of results.

Because the story of how skill accumulation varies with resource abundance is one of the

questions motivating this study, the linear programming problem described above is modified to allow for

the endogeneity of human capital accumulation. As a result, concomitant with determining output and

Peter K. Schott

18

wages, the program also chooses the optimal mix of high and low skill workers at any given level of

capital abundance. We assume that the schooling required to turn a low skilled worker into a high skilled

worker absorbs about 20% of a worker’s productive life5. Except for this lost work time, low-skilled

workers are allowed costlessly to be turned into high skilled workers. Thus we write the labor constraint

as:

12. H L vL+ = ,

where vL

is the total number of worker-years in the economy and L and H are the (endogenously

determined) number of low-skilled and high-skilled worker-years, respectively. A community that opts

for all H ends up with 20% fewer worker-years than a community with all L. We simply add this

constraint to our four factor linear programming problem as follows:

Primal Constraints

Aq v

A

A

A

A

0

qC

K

L

H

≤

−−

≤

0 0

0 0

0 1

1 0

12 1

0

0

.

H

L

v

v

v

C

K

L

Dual Constraints

5 Attaining a college education in the United States takes approximately 16 years, roughly one fifth of a 70 to 80

year work life. Qualitative implications of the simulation are not sensitive to variations in this assumption.

Peter K. Schott

19

A' w p

A A A A 0 pC K L H

≤

≤

0

0

0

0

0

0

0

-1

-1

0

1.2

1

w

w

w

w

w

C

K

H

L

L

,

where Ai are the input vectors for factor i, C and K represent cropland and capital, respectively, and 0 is a

vector of zeros of the same length as p and q.

This represents what looks like a rather minor change in the linear program, but it makes the

solution change in an important way. With cropland, physical capital, high-skilled workers and low-

skilled workers, the number of factors of production is four and the solution will usually involve the

output of four products. But the fungibility of H and L supports the movement of the endowment point to

the edge of a cone of diversification, and the number of products reduces to three. To put it differently,

there are really only three inputs: capital, land and labor. The economy then divides labor into high and

low skill categories as part of the maximization problem.6

Not all of the aggregates listed in tables 3.1.1 and 3.1.3 are included in the simulation because,

unless input combinations and prices are just right (which is not too likely with aggregate data), not all

goods will be selected by the linear program for production. The sectors that are included are listed in

table 3.2.1.7 Three differences between table 3.2.1 and the data listed in earlier tables deserve comment

6 An alternate approach is to run the linear program with a fixed level of human capital for each country. Though

this has the benefit of allowing the ratio of high to low skill workers to vary endogenously, it seems more satisfying

to allow the number or workers to adjust. We are currently working on an alternative between these two extremes.

7 How do we choose which sectors to include in the simulation? First, we exclude tobacco; as an extremely high

value added to capital sector, it generally is produced to the exclusion of virtually all other sectors. Second, we

exclude any remaining dominated sectors, defined as sectors that will not be produced even if a country’s

Peter K. Schott

20

before continuing. First, because of differences in product mix as well as other factors, the applicable

price (i.e. value added) for a given manufacturing sector is likely to be higher in developed versus

developing countries. Experimentation using both the value added per worker figures listed in table 3.1.1,

which are based on the labor-weighted world averages, as well as those for several agriculturally intense

developing countries, such as Colombia, Guatemala and Mexico, indicated that the latter provide more

realistic results in terms of what is produced at given levels of capital intensity, and are therefore included

in the simulation. If the price of industrial chemicals is very high, for example, countries produce it

immediately, rather than moving through a ladder of development. Thus, developing country prices are

selected to allow for such development.

Figure 3.2.1: Simulation Assumptions (All Quantities are Per Worker)Beans Mangos Food Beverage Apparel Textiles Trans Chemicals

CropLand (Hectares) 5.00 2.53 2.59 1.50 0.00 0.00 0.00 0.00Capital (US $) 119 8,644 14,566 13,493 904 3,712 9,367 22,865

Low Skill 1.00 1.00 0.69 0.58 0.84 0.79 0.54 0.43High Skill 0.00 0.00 0.31 0.42 0.16 0.22 0.46 0.57Price (US $) 1,432 33,624 50,095 43,028 3,161 12,000 29,589 39,661

Price/Capital 12.1 3.9 3.4 3.2 3.5 3.2 3.2 1.7

Second, the input requirements for the food processing and beverage sectors included in the

simulation are derived by adding the capital and cropland requirements for sugar and coffee to that of the

food (ISIC 311) and beverage (ISIC 314) figures given in table 3.1.1. This adjustment should be

interpreted as compressing into food processing both the raising of a crop and the processing and

endowments match exactly the input requirements of the sector. (Thus, being dominated indicates that some linear

combination of other sectors will always be superior to the dominated sector.) Non-dominated sectors are reported

in table 2.3.4. Note that not all of the sectors in this table are actually produced in the simulation because, with

endogenous human capital formation, there is no guarantee that country endowments will match a given sector’s

input requirements closely enough to make its production optimal.

Peter K. Schott

21

packaging of it. Our motivation for this adjustment is to create a linkage between food processing and

agriculture, thereby rendering land abundant country development paths more realistic. Finally, note that

we use the input and price data from Beans in table 3.1.3 to represent a peasant agriculture sector in the

development stories presented below.

To provide a visual context for comparing the simulation sectors, figure 3.2.1 plots them on an

endowment simplex anchored by labor, high skill and capital. You can see that mangoes are moderately

capital intensive but use no skill at all. Food processing has a skill intensity that is greater than apparel

and textiles but less than chemicals and transportation. As our simulated countries accumulate capital,

they will pick a path between these industry points. We consider three types of countries to help us

understand the differential effects of natural resource abundance: Super Abundant, Abundant and No

Land, with cropland per worker ratios of 6, 1.67 and 0 hectares, respectively. A cropland per worker ratio

of 6 hectares is quite large: only one country in our sample, Australia, has an intensity this high, and it is

almost twice as large as the next highest country in the sample, Canada.

Peter K. Schott

22

Figure 3.2.2

Sectors Included in the Simulation

Labor

High Skill

Capital0.04 0.10 0.20 0.40 1.00

0.01

0.02

0.04

0.08

0.20 1.00

2.50

5.00

10.00

25.00

Beans Mangos

Food

Bev

AppTex

Trans

Steel

IndCh

Labor / High Skill High Skill / Capital

Labor / Capital

Figures 3.2.2 and 3.2.3 provide a summary of two of the key implications of the simulation, both

of which mirror reality. Figure 3.2.2, which plots the ratio of high skill to total workers as capital per

worker accumulates, indicates that natural resource abundance leads to a greater delay in the emergence

of skilled workers. Of course, this result is due to the assumption that agriculture requires very low levels

of skill; since only resource abundant countries choose to produce agricultural goods because of their

natural advantage in land, the associated lower demand for skill deters workers from seeking an

education. As indicated in the figure, while the skilled jump to 20% of the population at the outset in the

No Land country, they remain 0% of the population until $4,000 and $6,000 capital per worker in the

Abundant and Super Abundant countries, respectively.

Peter K. Schott

23

Figure 3.2.3: Ratio of High to Low Skill Workers vs Capital per Worker ($000)

5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Per

cent

Hig

h S

kill

Super AbundantAbundant No Land

Figure 3.2.3 plots the evolution of income inequality, here measured as unity less the ratio of low

skill worker GDP share to low skill worker population share. Thus, a measure of zero indicates perfect

equality.8 Our assumption in using this definition is that low skill workers own neither capital nor land,

and therefore do not receive any of the GDP earned by these factors. The figure has several interesting

features. First, income inequality declines with capital accumulation, though not monotonically,

suggesting that periods of rising inequality, such as those currently being experienced by some countries,

are not ruled out by theory. What causes the ups and downs in each series? As will become clearer

below, these movements are due to the interaction between workers’ salaries and the steady accumulation

8 Recall that the ratio of high to low skill wages cannot be used here as a measure of inequality because it is fixed at

1.2 by assumption. By using the ratio of low skill workers to total possible workers, vL

, in the denominator, this

measure “corrects” for the 20% wage inequality built into the model by assumption.

Peter K. Schott

24

of capital built into the model. Large drops in inequality are the result of jumps in salary associated with

increased worker scarcity as countries transition to cones requiring more labor. Slow rises in inequality

after these transitions are due to the incremental increases in per worker capital: within a cone, rewards

are fixed, so as capital accumulates, it’s share will rise. Each up-down cycle is interestingly reminiscent

of the Kuznets curve.

Figure 3.2.4: Income Inequality versus Capital Per Worker ($000)

5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Low

Ski

ll G

DP

Sha

re /

Pop

ulat

ion

Sha

re

Super AbundantAbundant No Land

The second interesting feature of the figure is that income inequality decreases more rapidly in

the No Land country than in either of the land endowed economies. As we will see in a moment, this

result is a feature of more rapid industrialization: No Land sectors render labor more scarce earlier in

terms of capital accumulation than either of the land abundant countries, driving up wages and therefore

reducing the GDP share of land and capital.

Peter K. Schott

25

Finally, note that Super Abundant has the lowest income inequality at both very low and very

high levels of capital per worker. In general, this is due to the fact that in Super Abundant, land is so

plentiful that employing it has no cost.

Can we fit the current state of the world to these trends? Though the figure suggests that income

inequality can be lower in land scarce than in land abundant countries at the same per worker capital

intensity, it is perhaps more accurate to compare countries at different stages of development. Since the

US, for example, has approximately four times the per worker capital of most Latin American countries,

one should contrast the income inequality at the latter stages of the No Land with the income inequality at

the early stages of Abundant. In this manner, the results do make sense: Brazil and other land abundant

countries tend to have very high (and rising) measured income inequality, while Taiwan and other land

scarce countries tend to have lower inequality.

Tables 3.2.2 and 3.2.3 detail the linear program’s results by noting how product mix and wages

evolve with capital accumulation. Each table contains three panels, one for each country type; the top

row of each panel contain the per worker capital accumulation index, in $2000 increments. Development

paths are outlined by the sequence of boxes outlining the cones of diversification through which each

country type passes. Note that each box contains a different set of sectors (table 3.5) or factor rewards

(table 3.6). Thus, for example, table 3.2.2 reveals that Super Abundant produces beans and mangos from

$2000 to $8000 of per worker capital, while table 3.2.3 indicates that the rewards to cropland, capital,

high and low skilled workers in this cone are $0, 377%, $960 and $0, respectively.9 In addition, the last

9 Why are capital returns so high? This feature of the results is driven by the high price (valued added) to capital

ratios in our underlying data. Another look at table 3.2.1, for example, indicates that this ratio ranges from 12.05 for

beans to 1.73 for chemicals. If capital is scarce and labor and land are so abundant that their rewards are driven to

zero, it is no surprise that capital returns can be 300% or more. Such ratios are a feature of the Guatemalan

agricultural and UNIDO manufacturing data used in this simulation: very rarely does the capital requirement exceed

value added, which is what one might expect for interest rates on the order of 10%-20%. Interestingly, similar value

Peter K. Schott

26

two rows of each panel in table 3.2.2 exhibit the endogenous choice of high and low skill workers, while

the last row of each panel of table 3.2.3 shows the path of income inequality.

Table 3.2.1: Output Mix versus Capital AbundanceSuper Abundant

K/L 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000 22,000 24,000 26,000Beans 78 54 31 8Mangos 22 46 69 92 73 34Food Proc 25 62 94 94 94 94 94 94 94BeverageApparelTextileTransportChemicalsHigh Skill 8 19 29 29 29 29 29 29 29Low Skill 100 100 100 100 91 77 65 65 65 65 65 65 65

AbundantK/L 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000 22,000 24,000 26,000Beans 22 10Mangos 23 46 66 66 40 2Food Proc 26 63 41 64 64 64 64 64 64Beverage 41Apparel 32Textile 12Transport 20 30 29Chemicals 11 28 28 28 28 28 28High Skill 5 12 22 33 36 36 36 36 36 36 36Low Skill 45 56 93 86 74 61 57 57 57 57 57 57 57

No LandK/L 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000 22,000 24,000 26,000BeansMangosFood ProcBeverageApparel 56Textile 40 86 48 11Transport 9 45 81 81 65 50 35 19 4Chemicals 11 26 41 56 71 86 90 90 90High Skill 18 23 31 40 43 45 46 48 49 51 51 51 51Low Skill 79 73 62 52 48 46 45 43 41 39 39 39 39

High risk cones are shaded.

added to capital ratios are evident in the US data contained in the NBER Productivity Database. Thus, it appears as

though the high capital returns are likely due to a combination of underestimated capital stocks and incomplete

refinement of value added. Thus, though it is possible to “artfully” scale down interest rates to acceptable levels by

arbitrarily adjusting these numbers, it seems more palatable to let the numbers stand as a reminder of the vagaries of

data analysis.

Peter K. Schott

27

Table 3.2.2: Factor Rewards versus Capital AbundanceSuper Abundant

K/L 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000 22,000 24,000 26,000Crop Wage 0 0 0Capital Wage 3.77 2.68 0Low Skill Wage 960 10,420 47,170High Skill Wage 0 12,505 56,604

AbundantK/L 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000 22,000 24,000 26,000Crop Wage 191 1,315 2,485 2,495 6,363 4,528Capital Wage 3.83 3.50 3.11 2.72 0.66 0Low Skill Wage 0 0 432 3,734 22,635 36,127High Skill Wage 0 0 519 4,480 27,162 43,352

No LandK/L 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000 22,000 24,000 26,000Crop WageCapital Wage 3.14 0.76 0Low Skill Wage 314 20,607 36,127High Skill Wage 377 24,728 43,352

High risk cones are shaded.

To aid in interpreting the large amount of information conveyed in each of these tables, we

provide a short development story for each country type:

Super Abundant

In Super Abundant countries, land is so plentiful that it’s free, allowing peasants to earn the

relatively large income of about $1000 a year planting beans in the economy’s earliest stages. As

capital accumulates and becomes cheaper, inequality temporarily worsens as the country’s few

capitalists increase the size and output of their mango plantations, but drawing more and more

peasants off their small plots in the process. With even more capital, plantation owners are able

to diversify into food processing. This push into agribusiness creates a greater demand for low

and high skill labor, causing wages to jump, income inequality to drop and more low skilled

workers to enter school. Further capital accumulation causes a temporary increase in income

equality, but the country’s specialization in agribusiness soon raises wages even further,

Peter K. Schott

28

eliminating inequality altogether. Indeed, Super Abundant workers are so highly paid, and land is

so cheap, that industrialization beyond food processing is not viable.

Abundant

Land Abundant peasants have the hardest time earning a living. At the economy’s earliest stages,

after renting land and the few tools needed to work it, virtually no money is left. Fortunes

increase and inequality declines as more capital stimulates first mango plantations and then the

emergence of manufacturing, including apparel, textiles and transportation. With little demand

for skill, few workers send their children to school.

Further capital accumulation drives down its return, improves inequality and opens up further

opportunities in food processing, beverages and transportation. After a brief period where the

returns to landowners spike as agricultural activity peaks, wages jump, inequality declines further

and manufacturers’ demand for skill lures even more young to attend school. Eventually, skill

levels and capital are high enough to encourage entry into industrial chemicals, a premier

industry, causing additional salary gains and inequality declines. However, the presence of

wealthy landowners precludes Abundant low skill workers from achieving the same level of

equality as their Super Abundant counterparts.

No Land

In No Land, the soil is not suitable for farming, so peasants are immediately employed in the

producing of apparel and textiles. The people are poor relative to the inhabitants of Super

Abundant (they earn just one third the income), but are better off than their counterparts in

Abundant. Wages respond slowly to increasing activity in textiles and transportation, but the skill

needed in these sectors encourages many low skilled workers to attend school. The great demand

for low and high skill workers in the chemicals sector at per worker capital of $10,000 finally

Peter K. Schott

29

causes wages to spike and inequality to decline sharply, though inequality thereafter increases for

a time as owners of capital expand their businesses. The specialization in chemicals that

coincides with elimination of capital’s reward results in another jump in wages, eliminating

income inequality altogether.

The main theme of all three stories is that the demand labor associated with industrialization

benefits low skill workers by raising their salaries and driving down the return to capital. The next

section discusses how risk may inhibit the investment upon which this industrialization depends.

3.3 Agriculture Concentration and Capital Risk

Though illuminating, running the simulation as if the accumulation of capital in each country

were inevitable contradicts an important aspect of reality, which is that product price uncertainty can

increase a cone’s capital risk and thereby inhibit capital accumulation. Recall that these high-risk cones

can occur where insufficient diversification into manufacturing allows the return to capital to be imperiled

by natural resource product price uncertainty.

Table 3.2.2 uses shading to identify potential high risk cones, signaled here by the production of a

greater number of agricultural commodities than manufactured commodities. Because Super Abundant

never moves into non-resource manufacturing, its entire development path is high risk. The same is

almost true for Abundant, which has just two cones, at $6,000 and $8,000 capital per worker, with

sufficient diversification.

To estimate whether the risk-return tradeoff in high risk cones might be less attractive to domestic

and global investors than in diversified cones, we can use Stolper-Samuelson relationships presented

earlier to calculate the expected reward and variance of each factor along each country’s path of

development:

Expected Return: E(w) = (A’)-1 E(p)

Peter K. Schott

30

Variance: Var(w) = (A’)-1 Var(p) (A)-1

The first step in performing these calculations is to associate each of the sectors in the simulation

with the price series of an actual commodity.10 Then, like above, we calculate s year ahead price forecasts

and forecast standard errors by running an Ordinary Least Squares regression for each price index (US

PPI deflated) of the form

p pt t= + +−α β ε1 (3.3.1)

where pt is the deflated price index of a given commodity at year t. For any given price index, the

forecast and forecast standard error are

µ β µ+ −5 ( )pT (3.3.2)

and

σ β2 2

1

1

1+

=

−

∑ n

n

s

, (3.3.3)

respectively, where s is the number of years in the future to be forecast, m is the average price over price

series, pT is last observation in the series, and b and s are coefficient and regression standard error of the

autoregressive forecast. To calculate the covariance matrix Var(p), hereafter referred to as S, a hybrid

10 Agricultural prices are gathered from various world spot market indexes, while manufactured goods prices are

based upon US shipment deflators in Bartelsman, Becker and Gray (1994). Both sources contain annual

observations for 1970 to 1993.

Peter K. Schott

31

forecasting-seemingly unrelated regression framework is employed. Diagonal elements of S contain the

forecasting variance for the particular commodity, calculated as above. Off-diagonal elements, on the

other hand, are equal to the appropriate product of residual vectors from equation (2.1) divided by degrees

of freedom, df. Thus, the (m,n) elements of S are:

ε εm n

df

'

for m n≠ .

Table 3.3.1 details the particular proxy good chosen to represent each of the simulation sectors, as

well as their forecasted price (in terms of value added per worker) and forecasting error11.

Table 3.3.1

Sector Proxy Good Forecast Price Forecast ErrorBeans - 1,409 309

Mangos - 33,580 7,083Food Processing Processed Sugar 50,095 2,651

Beverage Roasted Coffee 42,951 5,405Apparel Underwear 3,163 86Textiles Warp Knit 11,993 195

Transportation Motor Vehicle Parts 29,586 732Chemcials Industrial Gases 40,246 1,780

Proxy Goods Used for Calculating Risk and Return by Cone

Table 3.3.2 provides a breakdown of the expected return and standard deviation of the capital

reward for each cone in each of the three countries’ paths of development using these price indexes. Each

cell in the table depicts the expected capital wage as well as its forecasting error. In addition, the vertical

11 The forecasted price and error result from combining the value added per worker data from tables 2.3.1 and 2.3.3

with the respective price indexes.

Peter K. Schott

32

length of each cell indicates the range of capital per worker for which it remains operative. Thus, for

example, the Beans-Mangos cone of Super Abundant has an expected return and standard error of 377%

and 614%, respectively, and it remains operative from $2,000 to $8,000 capital per worker. The total

vertical length of each country’s cones indicate the amount of capital per worker necessary to drive the

expected return of capital to zero. Thus, a zero expected return occurs at $14,000, $16,000 and $24,000

for Super Abundant, Abundant and No Land, respectively.

Table 3.3.2: Risk-Return Profile by Cone of DiversificationSuper Abundant Abundant No Land

K/L Sectors Return Risk Sectors Return Risk Sectors Return Risk

2,000 Apparel 3.14 0.47Textiles

Beans 3.83 3.28

4,000 Mangos

Beans 3.77 3.28

6,000 Mangos Mangos 3.50 0.16 Textiles 3.11 0.37Apparel Transportation

8,000 Mangos 3.11 0.37

TextilesTransportation

10,000Mangos 2.72 1.98

Mangos 3.13 1.65 Food

12,000 Food Transportation

14,000 Food 0.66 3.11

Beverages Transportation 0.76 0.28Chemicals Chemicals

16,000

18,000

20,000

22,000

High risk cones are shaded.

Peter K. Schott

33

Two trends in the table stand out. The first is that the non-diversified cones of the land endowed

countries, which have been shaded, are indeed riskier than the manufacturing-diversified cones. Second,

risk-adjusted returns are higher in diversified cones. All else equal, this suggests that countries in these

cones are more likely to have higher investment. The most attractive cones in this dimension are the

Mangos-Apparel cone of Abundant and the Textiles-Transportation / Mangos-Textiles-Transportation

cones Abundant and No Land, which are equivalent. These latter two cones are the same even though

Abundant also produces Mangos because neither Textiles nor Transportation require land. As a result,

the risk and return to capital are completely insulated from Mango price volatility in the manner

suggested by theory in section 2.

Of course, investors care about diversification across assets as well as the risk-return

characteristics of any individual investment. Thus, the allocation of world investment across cones of

diversification also depends upon how the returns of different cones co-vary. Investors, for example,

might seek investment in high risk, land abundant cones if the capital rewards in these cones are

negatively correlated with rewards in lower risk, land scarce cones. Indeed, we know from basic finance

that given Ω , the covariance matrix of cone returns, we can determine the share of investment that will

flow to each of the non-redundant cones above for any desired level of risk or return. This is done by

computing optimal portfolio weights to minimize risk subject to two constraints: first, that the portfolio

return is equal to some target return, r*; and second, that the vector of weights, s, which represent the

share of investment flowing to each cone, sum to unity. More formally, the global investor’s problem is

to

min ' ' * 'w

s s s r r s iΩ st and ≥ = 1 ,

where r is the vector of cone returns and i is a vector of ones. The solution to this problem for a range of

r* traces out the efficient risk-return portfolio frontier:

Peter K. Schott

34

s r i= − −−1

21

1 2Ω ( )λ λ

where i is a vector of ones of the appropriate length and λ1 and λ2 are solved via the system:

λλ

1

2

1 1

1 1

1

1

=

−−

− −

− −

−r r r i

i r i i

r' '

' '

*Ω ΩΩ Ω

.

In our case, the covariance matrix of cone returns, Ω , is equal to

v v

v v

v v

v v

c

j jc

c

j jc

11 1

1

11 1

1

. .

. .

. .

' . .

. .

. .

Σ

where vjc is the appropriate capital element for good j of the inverted A matrix if good j is produced in

cone c and zero otherwise.12 Thus, just as factor rewards are insensitive to output within a particular cone,

so is factor risk.

Figure 3.3.1 presents the results of these calculations, plotting the efficient portfolio frontier as

well as each of the non-redundant cones from the simulation. Table 3.3.3 provides the cone covariance

matrix, Ω , used to calculate this frontier. With this information, we are now able to examine how global

investors might allocate investment among cones. We employ to two different thought experiments.

12 Note that a distinct W matrix can be computed for each factor.

Peter K. Schott

35

Figure 3.3.1: Efficient Frontier of Cone of Diversification Assets

Capital Risk vs Return for All Cones

Food,Bev,Chem

Beans,Mangos

Mangos,Food,Trans

Mangos,Food

Trans,Chem

Text,TransApp,Text

Mangos,App

0

2

4

6

8

0 1 2 3 4

Capital Risk (%)

Cap

ital

Ret

urn

(%)

EfficientFrontier

Table 3.3.3: Cone Covariance Matrixmangos,food beans,mangos mangos,food,trans food,bev,chm mangos,apparel app,text text,trans trans,chm

mangos,food 2.74

beans,mangos -4.20 10.73

mangos,food,trans -0.02 0.05 0.02

food,bev,chm 3.15 -5.93 -0.03 3.92

mangos,apparel -0.03 4.53 -0.06 -1.19 9.69

app,text -0.12 0.42 0.01 -0.20 0.26 0.22

text,trans 0.17 -0.41 0.00 0.27 -0.16 -0.08 0.14

trans,chm -0.03 0.26 0.00 -0.10 0.26 0.01 -0.04 0.08

High risk cones are shaded.

First, assume that the world consists of many countries and that they are spread throughout all the

cones generated by the simulation. Table 3.3.4 details how new investment would be allocated among

these cones. The two header-rows of the table trace out the efficient portfolio frontier (return in the first

row, risk in the second) while the next eight rows indicate the share of investment that would flow to each

cone given a particular frontier risk-return combination. For example, if investors desired a return of

250%, they would place 90% of their investment into the non-diversified Mangos-Food-Transportation

Peter K. Schott

36

cone and 67% into the non-agriculture Textiles-Transportation cone. Note that several cones have

negative allocation shares, which, for equities, is interpreted as selling short. In this context, the

appropriate interpretation of short selling is hiring capital in one market and letting it in another, which

reverses payment streams in the same manner as selling a stock short.13 Thus, investors seeking a return

of 250% would like to hire capital in the Beans-Mangos and Food-Beverages-Chemicals cones and let it

elsewhere. The sub-totals at the bottom of the table summarize the share of investment flowing to high

risk and diversified cones. As expected, higher returns necessitate greater investment in high-risk cones.

Table 3.3.4: Optimal Portfolio of Diversification Cone Assets2.500 2.750 3.000 3.250 3.500 3.750

Cone 0.102 0.104 0.108 0.116 0.125 0.137mangos,food 0.90 -0.10 -1.10 -2.10 -3.09 -4.09

beans,mangos -0.32 0.02 0.36 0.70 1.04 1.37mangos,food,trans 0.47 0.48 0.49 0.50 0.51 0.52

food,bev,chm -1.22 0.12 1.46 2.80 4.14 5.48mangos,apparel 0.00 0.00 0.00 0.00 0.00 0.00

app,text 0.22 0.08 -0.06 -0.21 -0.35 -0.49text,trans 0.67 0.16 -0.34 -0.85 -1.35 -1.86trans,chm 0.28 0.24 0.20 0.16 0.11 0.07

SummaryHigh Risk Cones -0.17 0.52 1.21 1.90 2.59 3.28Diversified Cones 1.17 0.48 -0.21 -0.90 -1.59 -2.28

Total 1.00 1.00 1.00 1.00 1.00 1.00

High risk cones are shaded.

13 If all investors wish to allocate investment in the same way, how will the market function? Though we cannot

answer such questions given the implicit assumption of agent homogeneity in our model, we nevertheless use its

outcomes as a signal of what investors would like to do.

Peter K. Schott

37

The high allocation toward high-risk cones even at low returns is somewhat puzzling. A priori,

we expected to see all diversified cone allocations positive and most high risk cones negative. The main

message of the table appears to be that investors’ taste for a diversified cone portfolio can mitigate capital

inhibition in resource intense economies, though, even so, the fate of super abundance is dire: due to

short-selling, their development process may not proceed beyond the first cone. An interesting feature of

the efficient frontier is the relatively low tradeoff between risk and return.

A second thought experiment seeks to understand how rest-of-world capital allocation affects

development in three types of emerging markets. That is, assume the existence of a set of rest-of-world

countries, spread throughout the cones, and that investors in this rest-of-world have, in some earlier stage

of their decision process, determined how to split their investment between mature and emerging markets.

How might this emerging market investment be allocated among our three countries? Here, too, we must

impose the strong assumption that a sufficiently large rest of world exists so that product prices are not

sensitive to investment.14 On the other hand, given the relatively large number of countries which have

recently embraced free markets and sought to attract capital from the developed world, this method of

setting up the problem is nicely suggestive.

14 Both of these thought experiments are quite dependent upon exogenous demand. One method of circumventing

such a strong assumption, unexplored as of yet, is to consider maximizing world GDP at each iteration of the

simulation by reallocating world capital among the three countries, subject to the constraint that at least the same

level of each commodity is produced as in the first run of our simulation above.

Peter K. Schott

38

Table 3.3.5: Optimal Allocation of Investment Among Emerging MarketsCone Allocations Along Portfolio Frontier

3.200 3.300 3.400 3.500 3.600 3.700 <- ReturnCone 0.571 0.921 1.341 1.783 2.232 2.686 <--Risk

beans,mangos 0.08 0.23 0.38 0.52 0.67 0.81app,text 0.92 0.77 0.62 0.48 0.33 0.19

Cone Allocations Along Portfolio Frontier3.100 3.200 3.300 3.400 3.500 3.600 <- Return

Cone 0.390 0.435 0.822 1.270 1.731 2.198 <--Riskbeans,mangos -0.01 0.13 0.27 0.40 0.54 0.68

text, trans 1.01 0.87 0.73 0.60 0.46 0.32

Cone Allocations Along Portfolio Frontier0.700 0.800 0.900 1.000 1.100 1.200 <- Return

Cone 0.270 0.289 0.340 0.412 0.496 0.586 <--Riskbeans,mangos -0.02 0.01 0.05 0.08 0.11 0.14

text,chm 1.02 0.99 0.95 0.92 0.89 0.86

Cone Allocations Along Portfolio Frontier2.800 2.900 3.000 3.100 3.200 3.300 <- Return

Cone 0.131 0.132 0.134 0.137 0.141 0.146 <--Riskbeans,mangos -0.01 -0.01 -0.01 -0.01 0.00 0.00

mangos,app 0.75 0.79 0.82 0.86 0.90 0.93trans, chem 0.25 0.22 0.18 0.15 0.11 0.07

Cone Allocations Along Portfolio Frontier1.700 1.800 1.900 2.000 2.100 2.200 <- Return

Cone 0.171 0.172 0.176 0.181 0.188 0.198 <--Riskbeans,mangos 0.00 0.01 0.01 0.01 0.02 0.02mangos,tx,tr 0.40 0.44 0.47 0.51 0.55 0.59trans, chem 0.60 0.56 0.52 0.47 0.43 0.39

Cone Allocations Along Portfolio Frontier1.200 1.300 1.400 1.500 1.600 1.700 <- Return

Cone 0.258 0.261 0.266 0.272 0.280 0.290 <--Riskmangos,food 0.06 0.08 0.09 0.11 0.13 0.14

mangos,food,trans 0.13 0.16 0.18 0.21 0.24 0.26trans, chem 0.81 0.76 0.72 0.68 0.64 0.60

sa1

sa2

a2

a1

a3a4

a5

n1

n2

n3

SA A N

sa1

sa2

a2

a1

a3a4

a5

n1

n2

n3

SA A N

sa1

sa2

a2

a1

a3a4

a5

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SA A N

sa1

sa2

a2

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a3a4

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SA A N

sa1

sa2

a2

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a3a4

a5

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SA A N

sa1

sa2

a2

a1

a3a4

a5

n1

n2

n3

SA A N

sa1

sa2

a2

a1

a3a4

a5

n1

n2

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SA A N

sa1

sa2

a2

a1

a3a4

a5

n1

n2

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SA A N

sa1

sa2

a2

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a3a4

a5

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SA A N

sa1

sa2

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SA A N

sa1

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SA A N

sa1

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SA A N

Peter K. Schott

39

Table 3.3.5 traces out the endogenous allocation of capital to our three countries assuming

investors seek minimum risk along the efficient portfolio frontier. (Minimum risk allocations are boxed.)

The table is broken into six panels, each of which contains a different frontier and associated allocation

shares depending upon which cone each of the three countries inhabits. This frontier and these shares are

computed using the appropriate rows of the cone covariance matrix, Ω , given above. Movement by each

country through cones is portrayed in an icon to the left of each panel that is designed to mimic the shape

of table 3.3.2. Note that only two investment opportunities are available if cones are redundant,15 and that

as one moves down the table, each successive panel indicates greater cumulative investment by rest-of-

world in the three country-types. The following paragraphs provide descriptive words for each panel to

ease interpretation:

Panel 1 In the beginning, low risk seeking investors put most of their investment into No Land.

Due to the negative correlation between Manufacturing and Agriculture returns (a

function of prices), however, Abundant and Super Abundant get some capital as investors

seek to diversify. The result is that No Land gets accumulates capital more quickly.

Panel 2 Due to its receipt of most of rest of world investment, No Land moves into its second

cone while Super and Abundant remain in their first. No Land is now even more

attractive than before: capital inflows to the land abundant countries cease. Indeed,

investors even seem willing to remove capital from land abundant countries and place it

in No Land.

Panel 3 As a result all the previous investment, No Land moves into its third cone. Rest of world

diversification into the resource rich economies decreases because returns from No

15 If cones are redundant, the experiment assumes allocated capital is split evenly among countries.

Peter K. Schott

40

Land’s sophisticated manufacturing sector are almost independent of agriculture.

Development of the land abundant countries will cease unless investors are willing to

accept higher levels of risk.

Panel 4 If investors are willing to seek more risk, Abundant eventually will receive enough

capital to move into a diversified manufacturing-agriculture cone. The higher return and

lower risk associated with this cone makes it attractive to investors, who now split most

of their investment between Abundant and No Land. The negative correlation of

Abundant’s manufacturing vis a vis Super’s agriculture prices provides investors with an

incentive to allocate a small level of investment in Super Abundant. Nevertheless, it

remains mired in its first cone.

Panel 5 Abundant soon moves into its third cone, which is also manufacturing-agriculture

diversified. It now attracts the bulk of investment.

Panel 6 Once Abundant acquires sufficient capital, however, its movement into capital intensive

agriculture (Mangos and Food) sets up a trap: the return to capital declines and its risk

shoots up. As a result, investors favor the much more stable, and mature, No Land, and

seek diversification in Super Abundant.

The big message in this experiment is that, absent demand changes, resource rich economies may

become trapped in a state of permanent underdevelopment, and the more resource rich a country is, the

Peter K. Schott

41

earlier it gets trapped.16 To the extent that these results capture real world dynamics, they indicate an

important problem for resource abundant economies seeking to industrialize by attracting outside capital.

4 Conclusions

This paper explores theoretically and via a Heckscher-Ohlin linear program whether the

emergence of manufacturing can be hampered by land abundance. It demonstrates that land abundance

may deter skill accumulation and raise income inequality, and that insufficiently diversified production

may create unfavorable capital risk-return profiles for resource rich countries, deterring investment. In

addition, it illustrates that the effect of such unfavorable profiles may be mitigated by international

investors’ desire for a balanced portfolio of diversification cone assets. More generally, the paper

provides an nice example of how a multi-sector, multi-factor linear program can be used to gain insight

into a variety of pressing problems in international trade and development.

16 Changes in demand can affect this outcome by driving up the prices of goods produced by resource rich

economies to the point that the risk adjusted return is internationally competitive.

Peter K. Schott

42

Appendix A: Data Description

Data Sources

Net Exports Statistics Canada World Trade DatabaseLabor force World Bank CD ROMEducation Barro and Lee (1994)Capital Maskus (1991), Song (1993) and Penn World TablesCrop and forest land Maskus (1991)Investment World Bank CD ROMTerms of trade World Bank CD ROMManufacturing inputs and value added INDSTAT3 database from UNIDO and

US Current Population SurveyManufacturing prices Bartelsman, Becker and Gray (1994)Agriculture inputs Leamer, Maul, Rodriguez and Schott (1998)Agriculture prices Various world spot market figures

OECD Code Country Abbrev OECD Code Country Abbrev OECD Code Country Abbrev5850 Argentina arg 1700 Greece grc 2200 Norway nor700 Australia aus 5230 Guatemala gtm 5510 Panama pan1000 Austria aut 6550 India ind 6830 Philippines phl1100 Belgium bel 1900 Ireland irl 2300 Portugal prt5790 Bolivia bol 6150 Israel isr 4950 South Africa zaf5770 Brazil bra 2000 Italy ita 2400 Spain esp100 Canada can 500 Japan jpn 6570 Sri Lanka lka5830 Chile chl 6170 Jordan jor 2500 Sweden swe5630 Colombia col 4650 Kenya ken 6630 Thailand tha5490 Costa Rica cri 6910 Korea kor 2700 Turkey tur1300 Denmark dnk 6750 Malaysia mys 2800 UK gbr5730 Ecuador ecu 4830 Mauritius mus 5870 Uruguay ury1400 Finland fin 5130 Mexico mex 200 USA usa1500 France fra 2100 Netherlands nld 5650 Venezuela ven1600 Germany deu 800 New Zealand nzl 4730 Zimbabwe zwe

Table A1

Peter K. Schott

43

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